Kutta Fehlberg Research Articles

IMPROVING PARALLEL SOLUTIONS FOR METHOD OF LINES TO 1-D HEAT EQUATION BY USING FIVE POINT FINITE DIFFERENE

The aim of the study is to explain the numerical solutions of the one dimensional (1-D) of heat by using method of lines (MOLs). In the (MOLs) the derivative is firstly transformed to equivalent 5 point central finite differences methods (FDM) that is also transformed to the ordinary differential equations (ODEs). The produced (ODEs) systems are solved by the well-known techniques method of ODEs such as the 4th Runge - Kutta method and Runge - Kutta Fehlberg. And since of the conversion of the second derivative to the equivalent of the 5 points FDM which led to an increase in the size of the system equations ODEs, and thus increased we have improved the performance of these (MOLs) techniques by introduce parallel processing to speed up the solution of the produced ODE systems. The developed parallel technique, are suitable for running on MIMD (Multiple Instruction Stream, Multiple Data Stream) computers.

Terrific effect of H2 on 3D free convection MHD flow of C2H6O2[sbnd]H2O hybrid base fluid to dissolve Cu nanoparticles in a porous space considering the thermal radiation and nanoparticle shapes effects

In this article, the physical aspects of natural convection magnetohydrodynamic flow of Cu/Ethylene glycol-water nanofluid past a porosity vertical stretching sheet under impact of thermal radiation, shape and slip factor and suction/injection process has been analyzed using Runge- Kutta Fehlberg fifth order (RKF 5) numerical method. The influence of variable, different parameters such as nanoparticles shape factor, named hexahedron and Lamina on temperature and velocity profiles are exemplified quantitatively through graphs. Outputs demonstrate thermal radiation impact causes to produce heat and increase the temperature profile by increasing nanofluid molecules energy. Lamina shape nanoparticle has a greater effect on increasing Nusselt number (Nu) compared to hexahedron.

Ferromagnetic Liquid Flow due to Gravity-Aligned Stretching of an Elastic Sheet

The flow of a ferromagnetic liquid due to gravity-aligned stretching of an elastic sheet in the presence of a magnetic dipole is considered. The fluid momentum and thermal energy equations are formulated as a six parameter problem and a numerical study is made using the shooting method based on Runge – Kutta Fehlberg and Newton Raphson methods. Extensive computation on the velocity and temperature profiles is presented for a wide range of values of the parameters. It was found that the primary effect of the magnetothermomechanical interaction is to decelerate the fluid motion as compared to the hydrodynamic case. The results have possible industrial applications in ferromagnetic liquid based systems involving stretchable materials.

Boundary Layer Flow of Ferrofluid over a Stretching Sheet in the presence of Heat Source/Sink

The boundary layer flow of ferrofluid over a stretching sheet with heat source is considered. It is assumed that the magnetic field is sufficiently strong enough to saturate the ferrofluid and the variation of magnetization with temperature can be approximated by a linear function of temperature difference. The boundary layer approximation is used and the transformed governing differential equations are solved using the Shooting technique based on Runge - Kutta Fehlberg and Newton Raphson methods. The effects of various parameters on velocity profiles and wall heat transfer are presented graphically. The results have possible industrial applications in liquid based systems involving stretchable materials.